2020/2021

2020/2021

DM270

ING-INF/05 (SISTEMI DI ELABORAZIONE DELLE INFORMAZIONI)

DIPARTIMENTO DI MATEMATICA 'FELICE CASORATI'

MATEMATICA

PERCORSO COMUNE

1°

Primo Semestre (01/10/2020 - 20/01/2021)

6

45 ore di attività frontale

English

SCRITTO

DE NICOLAO GIUSEPPE (titolare) - 2 CFU
DE NICOLAO GIUSEPPE (titolare) - 4 CFU

Matrix algebra; elements of probability: scalar and vector random variables; elements of statistics: estimators and their properties.

Knowledge of main learning methods for classification and regression, of their properties and limitations. Ability to translate an experimental learning problem into a statistical formulation and select an appropriate method for its solution.

Introduction: Supervised and Unsupervised Learning.
Statistical Learning: Statistical Learning and Regression, Curse of Dimensionality and Parametric Models, Assessing Model Accuracy and Bias-Variance Trade-off, Classification Problems and K-Nearest Neighbors.
Linear Regression: Simple Linear Regression and Confidence Intervals, Hypothesis Testing, Multiple Linear Regression, Model Selection, Interactions and Nonlinearity.
Classification: Introduction to Classification, Logistic Regression and Maximum Likelihood, Linear Discriminant Analysis and Bayes Theorem, Naive Bayes.
Resampling Methods: Estimating Prediction Error and Validation Set Approach, K-fold Cross-Validation, Cross-Validation: The Right and Wrong Ways, The Bootstrap.
Linear Model Selection and Regularization: Linear Model Selection and Best Subset Selection, Stepwise Selection, Estimating Test Error Using Mallow’s Cp, AIC, BIC, Adjusted R-squared, Cross-Validation, Shrinkage Methods and Ridge Regression, The Lasso, Principal Components Regression and Partial Least Squares.
Moving Beyond Linearity: Polynomial Regression, Piecewise Polynomials and Splines, Smoothing Splines, Local Regression and Generalized Additive Models.
Tree-Based Methods: Decision Trees, Classification Trees and Comparison with Linear Models, Bootstrap Aggregation (Bagging) and Random Forests, Boosting.
Support Vector Machines: Support Vector Classifier, Kernels and Support Vector Machines.
Unsupervised Learning: Unsupervised Learning and Principal Components Analysis, K-means Clustering.
The fallacies of learning: regression to mediocrity, the covariate shift, statistical significance vs practical significance, correlation is not causation, observational vs experimental studies.

Lectures, practical class.

Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning (Vol. 1, No. 10). New York: Springer series in statistics.

Written examination: two theory-based questions and two practical ones.

Written examination: two theory-based questions and two practical ones.